## Nugget’s Exocet

This post examines the exocet attributed to Allen Barker and enthusiastically vetted by New Players forum, as applied to the opening elimination in the Golden Nugget.  This example suggests a more direct definition for the exocet , and introduces a new sysudoku tactic.  On the GN, a simple starting method generates extensive AIC and nice loops in all of the exocet trials.  If this feature is characteristic of  exocets, it transforms them from candidate removers into sysudoku monster slayers.

My earliest posts introduced beginners to the double line exclusion, the most prevalent move in basic solving.  In the dublex, as I dubbed it, pencil marks in two lines of a stack of boxes exclude candidates in a third line, producing a clue or an aligned pair or triple.

In a way, it’s come full circle for me to call attention to the exocet, a much more complex and rare expression of a similar idea.  The definition has wavered some in the forums, but I’ll paraphrase the refined definition “champaign” posted January 25, 2012.  The Golden Nugget  exocet is marked below, on a sysudoku candidate grid.

Two aligned cells in a box, the exocet base, contain candidates of four numbers, and two  cells on the two other lines and two other boxes of the box stack, the exocet target,  each contain the same four candidates.  If it can be shown that for every possible solution of the base cells, the same two numbers are solutions of the target cells, then any extra candidates of the target cells can be removed.

Earlier versions required, for every base solution,  that one of the target cells be shown to contain a solution number , but that seemed to be refuted.

To apply champaign’s definition to the GN case:   The r12c7 base contains 1247. If, regardless of which two are the true base solution, the target solution is shown to match them, the 3 is removed!

Well, of course.  Matching the true base solution in the true target solutions leaves no room for 3 in r7c9.

Until the exocet can be defined without “can be shown”trials, we may as well acknowledge the trials and make their application wider, without weakening the conclusion.  Just say straight out that extra target candidates can likely be excluded by every possible solution of the base cells.

To me, general acceptance of the current exocet as a method undercuts any complaints anyone might have to human solving by trials. The exocet formation is a logical rationale for logically constructed  trials.  It joins the trials toolbox this blog has demonstrated for Sue de Coq verification, long AIC chains, and for coloring clusters generated by Medusa, by nice loop, and by pattern slicing.  In the exocet formation, the conditions placed on the numbers of candidates and locations of cells simply increase the likelihood that the trials are successful.

And for a monster, there is no reason to fret about the number or difficulty of the trials. The four candidate exocet takes at least 6 and possibly up to 12 trials, every one of which must be carried to the verification of the exocet definition.

With all the attention it has received, I was knocked over by what I learned by my own GN exocet trials to eliminate 3r7c9. First we try the base 12r12c7, triggering a naked quad removing 3r7c9 and more.  This gets rid of the extra 3. It doesn’t meet the requirements of champaign’s exocet definition, but it’s OK for the “extra candidate removal” definition.

But this and more is achieved when we ask of one of the base solution  candidates in a target holding the extra  digit, say the 1-candidate in (12347)r7c9 in this case, if not you, then who?  The chain addressing this question starts with a slink, and leads us a merry chase back to the target cell, confirming both solution digits in both target cells!

The gloriously long nice loop removes many candidates of the exocet digits, as well as the GN first elimination candidate.  Show me you’re still awake by identifying them.

As for the other potential base solutions,  21, 41 and 71 are impossible, so we next try 14. The 4 clue triggers its own naked quad, making 4r3c6, which 4-chains its way to 4r7c9, again satisfying the conventional and my looser requirements for the exocet.

There is no nice loop, but the AIC switches to a 1-chain and that reaches the r4c8 target.  It continues as a 4-chain to the other target and beyond.   The 1-chain portion of the AIC  even duplicates the 1-chain side of the 1,2 trial’s nice loop.  I just copied and pasted it onto this slide.

The 17 seems to be next trial in line.  The 17 solution doesn’t yield anything directly, but the exocet target starter method  works again.

At first glance, you might think these chains are generated by some sysudoku computer.  Be assured, there is no such thing.  Each link is obvious. It’s the completed chain that is impressively complex. And besides, the exocet requirement has us focused on a very limited objective.  I did not search for this loop.  I just followed it blindly to its amazing conclusion.

Well, on to 24, 27, 47, and their flips.  Just 6 more.  Tell you what.  You can enjoy completing the exocet removal requirements for next time.   I’ll provide grids with inference chain checkpoints.  Good deal?  By the way, you’ll get nice loops without committing to an order of the solution, i.e. by trying a naked pair of base solution digits, so there’s really only three more trials.